Potassium-40
K-40 · Potassium, Z = 19, A = 40
Potassium-40 (K-40) is slow enough to be handled as a material rather than as a trace: 2.65e+5 Bq/g, or 0.00000717 Ci/g, puts a gigabecquerel at 3.77 kg. Decay is by electron capture with beta-plus, half-life 1.248 × 10⁹ years, and shedding even one per cent of the activity takes 18.1 million years.
At 0.0183 mGy·m²/(GBq·h) the air kerma rate constant is 4.2× less than Cs-137 and 17× less than Co-60, placing it 57 of 96 photon emitters in this dataset. 1 GBq at 1 m reads 0.0183 mGy/h, and 1 Ci at the same distance 0.678 mGy/h.
2 lines clear the 20 keV cutoff, but one of them carries 90% of the dose rate. The leading one is 1460.8 keV at 100.0% of the total — its emission probability is 10.66%, which is also the highest.
This is a shield that has to be designed: 11.5 mm of lead for a factor of two and 38.2 mm for a factor of ten, or 17.8 mm of steel to halve it, at which point the mass of the shield is part of the problem. At 1 GBq and a metre it is already under 20 µSv/h with nothing in the way.
Half-life, specific activity and dose rate
| Half-life | 1.248 × 10⁹ years (3.938e+16 s) |
| Decay mode | electron capture with beta-plus |
| Specific activity | 2.65e+5 Bq/g (0.00000717 Ci/g) |
| Air kerma rate constant Γ (δ = 20 keV) | 0.0183 mGy·m²/(GBq·h) |
| Dose rate, 1 GBq at 1 m | 0.0183 mGy/h |
| Dose rate, 1 Ci at 1 m | 0.678 mGy/h |
| Kerma-weighted mean photon energy | 1461 keV |
1461 keV carries 100% of the dose rate
3 further lines below the 20 keV cutoff, the highest at 3.19 keV and 0.976% emission probability in all, are excluded here and from Γ. Why the two columns rank differently.
| Energy (keV) | Emission probability (%) | Share of dose rate (%) |
|---|---|---|
| 1460.82 | 10.66 | 99.99 |
| 511.00 | 0.002 | 0.01 |
11.5 mm of lead halves this spectrum
Solved numerically across all 2 lines, narrow beam. Why not one representative energy.
| Material | HVL (mm) | TVL (mm) | TVL / HVL |
|---|---|---|---|
| lead | 11.5 | 38.2 | 3.32 |
| tungsten | 7.07 | 23.5 | 3.32 |
| iron | 17.8 | 59.1 | 3.32 |
| copper | 15.9 | 52.8 | 3.32 |
| concrete | 56.2 | 187 | 3.32 |
| water | 119 | 395 | 3.32 |
| aluminum | 50.6 | 168 | 3.32 |
A single energy would give 3.32. What a spread of energies does instead.
Activity over geological time
Ten half-lives is 12.5 billion years. On any timescale a facility can be planned over the activity is constant — 100.00% is left after forty years — and the mean life 1/λ is 1.80 billion years.
| Elapsed | Fraction remaining |
|---|---|
| 1 half-life | 50.0 % |
| 2 half-lives | 25.0 % |
| 5 half-lives | 3.13 % |
| 10 half-lives | 0.0977 % |
| Time to fall to 10 % of today's activity | 4.15 billion years |
| Time to fall to 1 % | 8.29 billion years |
| Time to fall to 0.1 % | 12.4 billion years |
Limits of these dose rates
- 0.0183 mGy/h at a metre — bare point source, no capsule, no self-absorption.
- 11.5 mm of lead halves this spectrum, narrow beam, scatter not added back.
- Γ excludes 3 lines under 20 keV, carrying 0.976% of all emissions.
- What every sheet leaves out, internal dose included.
Gamma and decay calculators for K-40
Computed from the IAEA Nuclear Data Section — Livechart API (ENSDF) and the NIST X-Ray Mass Attenuation Coefficients. Derivations and citations.